Transportation is one of the most vital services in modern society. It makes most of the other functions of society possible. Real transportation systems are so large and complex that in order to build the science of transportation systems it will be necessary to work in many areas, such as: Modeling, Optimization and Simulation. We are interested in solutions for the so-called fleet-sizing-and-allocation problem (FSAP). Fleet sizing and allocation problems are one of the most interesting and hard to solve logistic problems. A fleet sizing and allocation problem consists of two interdependent parts. The fleet sizing problem is to determine a number of transportation units that optimally balances service requirements against the cost of purchasing and maintaining the transportation units. The allocation problem is dealing with the repositioning of transportation units to serve future transportation demand. To make the fleet sizing and allocation problem a little bit more tractable we concentrate on logistic systems with a special hub-and-spoke structure. We start with a very simple fleet sizing of one-to-one case. This case will cause us to focus attention on several key issues in fleet sizing. Afterwards, the generalization of the one-to-one system is the one-to-many system. As a simple example can serve the continuous time situation where a single origin delivers items to many destinations. For the case that items are produced in a deterministic production cycle and transportation times are stochastic. We also studied a hub-and-spoke problem with continuous time and stochastic demand. To solve this problem, based on Marginal Analysis, we applied queueing theory methods. The investigation of the fleet-sizing-and-allocation problem for hub-and-spoke systems is started for a single-period, deterministic-demand model. In that the model hub has to decide how to use a given number of TU’s to satisfy a known (deterministic) demand in the spokes. We consider two cases: 1. Renting of additional TU’s from outside the system is not possible, 2. Renting of additional TU’s from outside the system is possible. For each case, based on Marginal Analysis, we developed a simple algorithm, which gives us the cost-minimal allocation. Since the multi-period, deterministic demand problem is NP-hard we suggest to use Genetic Algorithms. Some building elements for these are described. For the most general situation we also suggest to use simulation optimization. To realize the simulation optimization approach we could use the software tool “Calculation Assessment Optimization System” (CAOS). The idea of CAOS is to provide a software system, which separates the optimization process from the optimization problem. To solve an optimization problem the user of CAOS has to build up a model of the system to which the problem is related. Furthermore he has to define the decision parameters and their domain. Finally, we used CAOS for two classes of hub-and-spoke system: 1. A single hub with four spokes, 2. A single hub with fifty spokes. We applied four optimizers – a Genetic Algorithm, Tabu Search, Hybrid Parallel and Hybrid Serial with two distributions (Normal Distribution and Exponential Distribution) for a customer interarrival times and their demand.

Materialfluss-Systeme für den Stückgut-Transport auf der Basis von Stetigförderern sind meist modular aufgebaut. Das Verhalten gleichartiger Materialfluss-Elemente unterscheidet sich durch technische Parameter (z.B. geometrische Größen) und durch unterschiedliche logistische Belastungen der Elemente im System. Durch die in der Arbeit getroffenen Modellannahmen werden für die Elemente nur lokale Steuerungsregeln zugelassen und für das System Blockierfreiheit vorausgesetzt. Das Verhalten eines Materialfluss-Elements hängt dann nicht mehr von Zuständen anderer Elemente des Systems ab sondern nur noch von den stochastischen Prozessen des Eintreffens von Transporteinheiten. Die Auslastung eines Elements, die Quantile der Warteschlangenlängen an seinen Eingängen und die Variationskoeffizienten seiner Abgangsströme sind statistische Kenngrößen. Sie hängen im Wesentlichen nur von der Klasse des Elements, seinen technischen Parametern, den Parametern der Eingangsströme und der lokalen Transportmatrix ab. Diese funktionellen Abhängigkeiten sind im Allgemeinen nicht analytisch handhabbar. Da diese Funktionen stetig differenzierbar und beschränkt sind und von relativ viele Eingansgrößen anhängen, sind neuronale Netze gut geeignet für numerische Näherungen. Mit Hilfe von einfachen neuronalen Netzen können die statistischen Kenngrößen numerisch approximiert werden. Aus einzelnen Teilmodellen kann ein hybrides Modell des gesamten Systems zusammengesetzt werden. Anhand von einigen Beispielen wird die Güte der Modellierung bewertet. / Material flow systems are normally built with a modular structure. The behavoir of similar elements only differs by technical parameters (e.g. geometriy), and by different logistic loads of the elements in the system. In this paper, a new model is being developed for a non-blocking system with non-global control rules. The behavior of a flow of a material flow element is assumed not to depend on the conditions of other elements of the system, but only on stochastic processes of the arrival of transportation units. The rate of utilization of an element, the quantiles of the queue lengths at its inputs, and the dispersion of its output stream are statistic characteristics. They depend only on the type of the element, its technical parameters, the parameters of the input streams, and the local transportation matrix. These functional dependencies are not analytically manageable. But due to their properties, neural nets are well suited for numeric approximations of these statistic functions. The single models can be used to compose a hybrid model of the whole system. A few examples show the quality of the new modeling technique.

Au cours des vingt dernières années, le secteur des services est devenu le secteur le plus important en nombre d'actifs occupés dans l’économie mondiale, en particulier dans les pays développés. Par ailleurs, la concurrence et la coopération dans le secteur des services sont devenues de plus en plus populaires dans le contexte de la mondialisation économique. Comment collaborer avec un accord gagnant-gagnant apporte une source fertile de problèmes de management des opérations dans le domaine des services. Dans cette thèse, nous étudions des stratégies de collaboration dans des systèmes de services homogènes. Nous nous concentrons en particulier sur les stratégies de pooling des ressources de service.Dans les deux premières parties, nous étudions le problème de partage des coûts entre les fournisseurs de services indépendants avec des temps de service qui suivent une distribution générale et en tenant compte de l'abandon des clients. Nous modélisons à la fois chaque fournisseur de services et la coalition coopérative comme des files d'attente avec serveur unique, et spécialisons les stratégies de pooling avec les capacités de services fixes et modifiables. Dans la dernière partie, nous abordons le problème de pooling dans le cadre multiserveur pour évaluer la qualité de l'hypothèse "superserveur". Nous étudions numériquement l'impact de la variabilité de la durée de service et l'abandon des clients sur les jeux de mise en commun des ressources. Nous comparons aussi les partages des coûts entre le système de "super-serveur" et multiserveur. / In past twenty years, the service sector has emerged as the primary sector in the world economy, especially in developed countries. Competition and cooperation in service industries have become more and more popular in the context of economic globalization. How to operate the collaboration with a win-win agreement brings a fertile source of operations management issues in service science. In this thesis, we study collaborations between homogeneous service systems in terms of resource pooling strategies.In the first two parts, we investigate the cost-sharing problem among independent service providers with general service times and accounting for the customer abandonment. We model both the service provider and the cooperative coalition as single server queues, and specialize the capacity pooling strategies with the fixed and optimized service capacities.Finally, we address the service pooling problem in the multi-serverpooling setting to assess the quality of the "super-server" assumption.We numerically investigate the impact of service duration variability and customer abandonment on the pooling game. We compare between cost-sharing results of the two resource pooling concepts, with or without the "super-server" assumptions.

Les réseaux de cinquième génération sont en cours de définition et leurs différentes composantes commencent à émerger: nouvelles technologies d'accès à la radio, convergence fixe et mobile des réseaux et virtualization.Le contrôle et la gestion de bout en bout (E2E) du réseau ont une importance particulière pour les performances du réseau. Cela étant, nous segmentons le travail de thèse en deux parties: le réseau d’accès radio (RAN) axé sur la technologie MIMO Massif (M-MIMO) et la connexion E2E du point de vue de la couche transport.Dans la première partie, nous considérons la formation de faisceaux focalisés avec un structure hiérarchique dans les réseaux sans fil. Pour un ensemble de flots donnée, nous proposons des algorithmes efficaces en terme de complexité pour une allocation avec alpha-équité. Nous proposons ensuite des formules exactes pour la performance au niveau du flot, à la fois pour le trafic élastique (avec une équité proportionnelle et équité max-min) et le trafic en continu. Nous validons les résultats analytiques par des simulations.La seconde partie de la thèse vise à développer une fonction de réseau auto-organisant (SON) qui améliore la qualité d'expérience (QoE) des connexions en bout-en-bout. Nous considérons un service de type vidéo streaming et développons une fonctionnalité SON qui adapte la QoE de bout-en-bout entre le serveur vidéo et l'utilisateur. La mémoire-tampon reçoit les données d'un serveur avec une connexion E2E en suivant le protocole TCP. Nous proposons un modèle qui décrit ce comportement et nous comparons les formules analytiques obtenues avec les simulations. Enfin, nous proposons un SON qui donne la qualité vidéo de sorte que la probabilité de famine soit égale à une valeur cible fixée au préalable. / Fifth generation networks are being defined and their different components are beginning to emerge: new technologies for access to radio, fixed and mobile convergence of networks and virtualization.End-to-end (E2E) control and management of the network have a particular importance for network performance. Having this in mind, we segment the work of the thesis in two parts: the radio access network (RAN) with a focus on Massive MIMO (M-MIMO) technology and the E2E connection from a point of view of the transport layer.In the first part, we consider hierarchical beamforming in wireless networks. For a given population of flows, we propose computationally efficient algorithms for fair rate allocation. We next propose closed-form formulas for flow level performance, for both elastic (with either proportional fairness and max-min fairness) and streaming traffic. We further assess the performance of hierarchical beamforming using numerical experiments.In the second part, we identify an application of SON namely the control of the starvation probability of video streaming service. The buffer receives data from a server with an E2E connection following the TCP protocol. We propose a model that describes the behavior of a buffer content and we compare the analytical formulas obtained with simulations. Finally, we propose a SON function that by adjusting the application video rate, achieves a target starvation probability.

Dans cette thèse, nous étudions le contrôle dynamique des systèmes de partage de ressources qui se posent dans divers domaines : réseaux de gestion des stocks, services de santé, réseaux de communication, etc. Nous visons à allouer efficacement les ressources disponibles entre des projets concurrents, selon certains critères de performance. Ce type de problème est de nature stochastique et peut être très complexe à résoudre. Nous nous concentrons donc sur le développement de méthodes heuristiques performantes. Dans la partie I, nous nous plaçons dans le cadre des Restless Bandit Problems, qui est une classe générale de problèmes d’optimisation dynamique stochastique. Relaxer la contrainte de trajectoire dans le problème d’optimisation permet de définir une politique d’index comme heuristique pour le modèle contraint d’origine, aussi appelée politique d’index de Whittle. Nous dérivons une expression analytique pour l’index de Whittle en fonction des probabilités stationnaires de l’état dans le cas où les bandits (ou projets) suivent un processus de naissance et de mort. D’une part, cette expression nécessite la vérification de plusieurs conditions techniques, d’autre part elle ne peut être calculée explicitement que dans certains cas spécifiques. Nous prouvons ensuite, que dans le cas particulier d’une file d’attente multi-classe avec abandon, la politique d’index de Whittle est asymptotiquement optimale aussi bien pour les régimes à faible trafic comme pour ceux à fort trafic. Dans la partie II, nous dérivons des heuristiques issues de l’approximation des systèmes stochastiques de partage de ressources par des modèles fluides déterministes. Nous formulons dans un premier temps une version fluide du problème d’optimisation relaxé que nous avons introduit dans la partie I, et développons une politique d’index fluide. L’index fluide peut toujours être calculé explicitement et surmonte donc les questions techniques qui se posent lors du calcul de l’index de Whittle. Nous appliquons les politiques d’index de Whittle et de l’index fluide à plusieurs cas : les fermes de serveurs éco-conscients, l’ordonnancement opportuniste dans les systèmes sans fil, et la gestion de stockage de produits périssables. Nous montrons numériquement que ces politiques d’index sont presque optimales. Dans un second temps, nous étudions l’ordonnancement optimal de la version fluide d’une file d’attente multi-classe avec abandon. Nous obtenons le contrôle optimal du modèle fluide en présence de deux classes de clients en concurrence pour une même ressource. En nous appuyant sur ces derniers résultats, nous proposons une heuristique pour le cas général de plusieurs classes. Cette heuristique montre une performance quasi-optimale lorsqu’elle est appliquée au modèle stochastique original pour des charges de travail élevées. Enfin, dans la partie III, nous étudions les phénomènes d’abandon dans le contexte d’un problème de distribution de contenu. Nous caractérisons une politique optimale de regroupement afin que des demandes issues d’utilisateurs impatients puissent être servies efficacement en mode diffusion. / In this thesis we study the dynamic control of resource-sharing systems that arise in various domains: e.g. inventory management, healthcare and communication networks. We aim at efficiently allocating the available resources among competing projects according to a certain performance criteria. These type of problems have a stochastic nature and may be very complex to solve. We therefore focus on developing well-performing heuristics. In Part I, we consider the framework of Restless Bandit Problems, which is a general class of dynamic stochastic optimization problems. Relaxing the sample-path constraint in the optimization problem enables to define an index-based heuristic for the original constrained model, the so-called Whittle index policy. We derive a closed-form expression for the Whittle index as a function of the steady-state probabilities for the case in which bandits (projects) evolve in a birth-and-death fashion. This expression requires several technical conditions to be verified, and in addition, it can only be computed explicitly in specific cases. In the particular case of a multi-class abandonment queue, we further prove that the Whittle index policy is asymptotically optimal in the light-traffic and heavy-traffic regimes. In Part II, we derive heuristics by approximating the stochastic resource-sharing systems with deterministic fluid models. We first formulate a fluid version of the relaxed optimization problem introduced in Part I, and we develop a fluid index policy. The fluid index can always be computed explicitly and hence overcomes the technical issues that arise when calculating the Whittle index. We apply the Whittle index and the fluid index policies to several systems: e.g. power-aware server-farms, opportunistic scheduling in wireless systems, and make-to-stock problems with perishable items. We show numerically that both index policies are nearly optimal. Secondly, we study the optimal scheduling control for the fluid version of a multi-class abandonment queue. We derive the fluid optimal control when there are two classes of customers competing for a single resource. Based on the insights provided by this result we build a heuristic for the general multi-class setting. This heuristic shows near-optimal performance when applied to the original stochastic model for high workloads. In Part III, we further investigate the abandonment phenomena in the context of a content delivery problem. We characterize an optimal grouping policy so that requests, which are impatient, are efficiently transmitted in a multi-cast mode.

A typical model for real-time status update systems consists of a transmitter node that generates real-time status updates about some physical process(es) of interest and sends them through a communication network to a destination node. Such a model can be used to analyze the performance of a plethora of emerging Internet of Things (IoT)-enabled real-time applications including healthcare, factory automation, autonomous vehicles, and smart homes, to name a few. The performance of these applications highly depends upon the freshness of the information status at the destination node about its monitored physical process(es). Because of that, the main design objective of such real-time status update systems is to ensure timely delivery of status updates from the transmitter node to the destination node. To measure the freshness of information at the destination node, the Age of Information (AoI) has been introduced as a performance metric that accounts for the generation time of each status update (which was ignored by conventional performance metrics, specifically throughput and delay). Since then, there have been two main research directions in the AoI research area. The first direction aimed to analyze/characterize AoI in different queueing-theoretic models/disciplines, and the second direction was focused on the optimization of AoI in different communication systems that deal with time-sensitive information. However, the prior queueing-theoretic analyses of AoI have mostly been limited to the characterization of the average AoI and the prior studies developing AoI/age-aware scheduling/transmission policies have mostly ignored the energy constraints at the transmitter node(s). Motivated by these limitations, this dissertation develops new queueing-theoretic methods that allow the characterization of the distribution of AoI in several classes of status updating systems as well as novel AoI-aware scheduling policies accounting for the energy constraints at the transmitter nodes (for several settings of communication networks) in the process of decision-making using tools from optimization theory and reinforcement learning. The first part of this dissertation develops a stochastic hybrid system (SHS)-based general framework to facilitate the analysis of characterizing the distribution of AoI in several classes of real-time status updating systems. First, we study a general setting of status updating systems, where a set of source nodes provide status updates about some physical process(es) to a set of monitors. For this setting, the continuous state of the system is formed by the AoI/age processes at different monitors, the discrete state of the system is modeled using a finite-state continuous-time Markov chain, and the coupled evolution of the continuous and discrete states of the system is described by a piecewise linear SHS with linear reset maps. Using the notion of tensors, we derive a system of linear equations for the characterization of the joint moment generating function (MGF) of an arbitrary set of age processes in the network. Afterwards, we study a general setting of gossip networks in which a source node forwards its measurements (in the form of status updates) about some observed physical process to a set of monitoring nodes according to independent Poisson processes. Furthermore, each monitoring node sends status updates about its information status (about the process observed by the source) to the other monitoring nodes according to independent Poisson processes. For this setup, we develop SHS-based methods that allow the characterization of higher-order marginal/joint moments of the age processes in the network. Finally, our SHS-based framework is applied to derive the stationary marginal and joint MGFs for several queueing disciplines and gossip network topologies, using which we derive closed-form expressions for marginal/joint high-order statistics of age processes, such as the variance of each age process and the correlation coefficients between all possible pairwise combinations of age processes. In the second part of this dissertation, our analysis is focused on understanding the distributional properties of AoI in status updating systems powered by energy harvesting (EH). In particular, we consider a multi-source status updating system in which an EH-powered transmitter node has multiple sources generating status updates about several physical processes. The status updates are then sent to a destination node where the freshness of each status update is measured in terms of AoI. The status updates of each source and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. For this setup, we derive closed-form expressions of MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and source-agnostic/source-aware preemptive in service strategies. The generality of our analysis is demonstrated by recovering several existing results as special cases. A key insight from our characterization of the distributional properties of AoI is that it is crucial to incorporate the higher moments of AoI in the implementation/optimization of status updating systems rather than just relying on its average (as has been mostly done in the existing literature on AoI). In the third and final part of this dissertation, we employ AoI as a performance metric for several settings of communication networks, and develop novel AoI-aware scheduling policies using tools from optimization theory and reinforcement learning. First, we investigate the role of an unmanned aerial vehicle (UAV) as a mobile relay to minimize the average peak AoI for a source-destination pair. For this setup, we formulate an optimization problem to jointly optimize the UAV's flight trajectory as well as energy and service time allocations for packet transmissions. This optimization problem is subject to the UAV's mobility constraints and the total available energy constraints at the source node and UAV. In order to solve this non-convex problem, we propose an efficient iterative algorithm and establish its convergence analytically. A key insight obtained from our results is that the optimal design of the UAV's flight trajectory achieves significant performance gains especially when the available energy at the source node and UAV is limited and/or when the size of the update packet is large. Afterwards, we study a generic system setup for an IoT network in which radio frequency (RF)-powered IoT devices are sensing different physical processes and need to transmit their sensed data to a destination node. For this generic system setup, we develop a novel reinforcement learning-based framework that characterizes the optimal sampling policy for IoT devices with the objective of minimizing the long-term weighted sum of average AoI values in the network. Our analytical results characterize the structural properties of the age-optimal policy, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. They further demonstrate that the structures of the age-optimal and throughput-optimal policies are different. Finally, we analytically characterize the structural properties of the AoI-optimal joint sampling and updating policy for wireless powered communication networks while accounting for the costs of generating status updates in the process of decision-making. Our results demonstrate that the AoI-optimal joint sampling and updating policy has a threshold-based structure with respect to different system state variables. / Doctor of Philosophy / A typical model for real-time status update systems consists of a transmitter node that generates real-time status updates about some physical process(es) of interest and sends them through a communication network to a destination node. Such a model can be used to analyze the performance of a plethora of emerging Internet of Things (IoT)-enabled real-time applications including healthcare, factory automation, autonomous vehicles, and smart homes, to name a few. The performance of these applications highly depends upon the freshness of the information status at the destination node about its monitored physical process(es). Because of that, the main design objective of such real-time status update systems is to ensure timely delivery of status updates from the transmitter node to the destination node. To measure the freshness of information at the destination node, the Age of Information (AoI) has been introduced as a performance metric that accounts for the generation time of each status update (which was ignored by conventional performance metrics, specifically throughput and delay). Since then, there have been two main research directions in the AoI research area. The first direction aimed to analyze/characterize AoI in different queueing-theoretic models/disciplines, and the second direction was focused on the optimization of AoI in different communication systems that deal with time-sensitive information. However, the prior queueing-theoretic analyses of AoI have mostly been limited to the characterization of the average AoI and the prior studies developing AoI/age-aware scheduling/transmission policies have mostly ignored the energy constraints at the transmitter node(s). Motivated by these limitations, this dissertation first develops new queueing-theoretic methods that allow the characterization of the distribution of AoI in several classes of status updating systems. Afterwards, using tools from optimization theory and reinforcement learning, novel AoI-aware scheduling policies are developed while accounting for the energy constraints at the transmitter nodes for several settings of communication networks, including unmanned aerial vehicles (UAVs)-assisted and radio frequency (RF)-powered communication networks, in the process of decision-making. In the first part of this dissertation, a stochastic hybrid system (SHS)-based general framework is first developed to facilitate the analysis of characterizing the distribution of AoI in several classes of real-time status updating systems. Afterwards, this framework is applied to derive the stationary marginal and joint moment generating functions (MGFs) for several queueing disciplines and gossip network topologies, using which we derive closed-form expressions for marginal/joint high-order statistics of age processes, such as the variance of each age process and the correlation coefficients between all possible pairwise combinations of age processes. In the second part of this dissertation, our analysis is focused on understanding the distributional properties of AoI in status updating systems powered by energy harvesting (EH). In particular, we consider a multi-source status updating system in which an EH-powered transmitter node has multiple sources generating status updates about several physical processes. The status updates are then sent to a destination node where the freshness of each status update is measured in terms of AoI. For this setup, we derive closed-form expressions of MGF of AoI under several queueing disciplines at the transmitter. The generality of our analysis is demonstrated by recovering several existing results as special cases. A key insight from our characterization of the distributional properties of AoI is that it is crucial to incorporate the higher moments of AoI in the implementation/optimization of status updating systems rather than just relying on its average (as has been mostly done in the existing literature on AoI). In the third and final part of this dissertation, we employ AoI as a performance metric for several settings of communication networks, and develop novel AoI-aware scheduling policies using tools from optimization theory and reinforcement learning. First, we investigate the role of a UAV as a mobile relay to minimize the average peak AoI for a source-destination pair. For this setup, we formulate an optimization problem to jointly optimize the UAV's flight trajectory as well as energy and service time allocations for packet transmissions. This optimization problem is subject to the UAV's mobility constraints and the total available energy constraints at the source node and UAV. A key insight obtained from our results is that the optimal design of the UAV's flight trajectory achieves significant performance gains especially when the available energy at the source node and UAV is limited and/or when the size of the update packet is large. Afterwards, we study a generic system setup for an IoT network in which RF-powered IoT devices are sensing different physical processes and need to transmit their sensed data to a destination node. For this generic system setup, we develop a novel reinforcement learning-based framework that characterizes the optimal sampling policy for IoT devices with the objective of minimizing the long-term weighted sum of average AoI values in the network. Our analytical results characterize the structural properties of the age-optimal policy, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. They further demonstrate that the structures of the age-optimal and throughput-optimal policies are different. Finally, we analytically characterize the structural properties of the AoI-optimal joint sampling and updating policy for wireless powered communication networks while accounting for the costs of generating status updates in the process of decision-making. Our results demonstrate that the AoI-optimal joint sampling and updating policy has a threshold-based structure with respect to different system state variables.

Yes / One of the main features of the third generation (3G) mobile networks is their capability to provide different classes of services; especially multimedia and real-time services in addition to the traditional telephony and data services. These new services, however, will require higher Quality of Service (QoS) constraints on the network mainly regarding delay, delay variation and packet loss. Additionally, the overall traffic profile in both the air interface and inside the network will be rather different than used to be in today's mobile networks. Therefore, providing QoS for the new services will require more than what a call admission control algorithm can achieve at the border of the network, but also continuous buffer control in both the wireless and the fixed part of the network to ensure that higher priority traffic is treated in the proper way. This paper proposes and analytically evaluates a buffer management scheme that is based on multi-level priority and Complete Buffer Sharing (CBS) policy for all buffers at the border and inside the wireless network. The analytical model is based on the G/G/1/N censored queue with single server and R (R¿2) priority classes under the Head of Line (HoL) service rule for the CBS scheme. The traffic is modelled using the Generalised Exponential distribution. The paper presents an analytical solution based on the approximation using the Maximum Entropy (ME) principle. The numerical results show the capability of the buffer management scheme to provide higher QoS for the higher priority service classes.

No / An analytic framework is devised, based on the principle of maximum entropy (ME), for the performance modelling and evaluation of a wireless GSM/GPRS cell supporting bursty multiple class traffic of voice calls and data packets under complete partitioning (CPS), partial sharing (PSS) and aggregate sharing (ASS) traffic handling schemes. Three distinct open queueing network models (QNMS) under CPS, PSS and ASS, respectively, are described, subject to external compound Poisson traffic processes and generalised exponential (GE) transmission times under a repetitive service blocking mechanism and a complete buffer sharing management rule. Each QNM generally consists of three building block stations, namely a loss system with GSM/GPRS traffic and a system of access and transfer finite capacity queues in tandem dealing with GPRS traffic under head-of-line and discriminatory processor sharing scheduling disciplines, respectively. The analytic methodology is illustrated by focusing on the performance study of the GE-type tandem queueing system for GPRS under a CPS. An ME product-form approximation is characterised leading into a decomposition of the tandem system into individual queues and closed-form ME expressions for state and blocking probabilities are presented. Typical numerical examples are included to validate the ME solutions against simulation and study the effect of external GPRS bursty traffic upon the performance of the cell. Moreover, an overview of recent extensions of the work towards the analysis of a GE-type multiple server finite capacity queue with preemptive resume priorities and its implications towards the performance modelling and evaluation of GSM/GPRS cells with PSS and ASS are included. / ,

This master's thesis deals with queueing theory and its application in designing node models in packet-switched network. There are described general principles of designing queueing theory models and its mathematical background. Further simulator of packet delay in network was created. This application implements two described models - M/M/1 and M/G/1. Application can be used for simulating network nodes and obtaining basic network characteristics like packet delay or packet loss. Next, lab exercise was created, in that exercise students familiarize themselves with basic concepts of queueing theory and examine both analytical and simulation approach to solving queueing systems.

本論文中，我們提出基於機場安全檢查的分層排隊理論模型，模型中的旅客基於歷史的安全數據被分成三組。我們運用二維馬可夫過程（two-dimensional Markov process）以及馬可夫調控卜瓦松過程（Markov modulated Poisson process）構建模型的排隊系統並加以分析。我們收集了台灣桃園國際機場和其它兩個機場的旅客數據以驗證我們提出的模型，並運用模擬退火法（simulated annealing）求得近似最佳解（near-optimum solution）。最後我們通過模型的旅客平均等候時間和另外兩種等候模型進行比較，之後得出我們的模型確實可以在不增加成本，甚至提升安全性的同時能夠有效地減少平均等候時間。 / This thesis proposes a tiered inspection system for airport security, wherein passengers are divided into three classes based on historical security records. A two-dimensional Markov process and a Markov modulated Poisson process (MMPP) queue were used in the formulation of the security inspection system. Simulated annealing was then used to obtain near-optimum solution for the model. The efficacy of the proposed model was evaluated using the arrival data of passengers at Taoyuan International Airport and other two international airports. A comparison with two conventional queueing models with regard to the average waiting time demonstrated the effectiveness of the proposed security inspection system in enhancing service efficiency and boosting the level of security.